New applications of non-hermitian random matrices

Details New applications of non-hermitian random matrices New applications of non-hermitian random matrices

2002-10-15

arxiv.org/abs/cond-mat/0210331v1

Annales Henri Poincare 4 (2003) S851-S861

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

10 pages, 3 figures, Talk given at TH-2002, Paris, UNESCO, July 2002

Scientific paper

10.1007/s00023-003-0966-2

We discuss recently discovered links of the statistical models of normal random matrices to some important physical problems of pattern formation and to the quantum Hall effect. Specifically, the large $N$ limit of the normal matrix model with a general statistical weight describes dynamics of the interface between two incompressible fluids with different viscousities in a thin plane cell (the Saffman-Taylor problem). The latter appears to be mathematically equivalent to the growth of semiclassical 2D electronic droplets in a strong uniform magnetic field with localized magnetic impurities (fluxes), as the number of electrons increases. The equivalence is most easily seen by relating the both problems to the matrix model.

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